LCALCEPS-tag: Macroscopic dielectric properties and Born effective charge tensors

LCALCEPS=.TRUE. (Available as of VASP.5.2)

VASP calculates the ion-clamped static dielectric tensor

$$\epsilon^\infty_{ij}=\delta_{ij}+ \frac{4\pi}{\epsilon_0}\frac{\partial P_i}{\partial {\mathcal E}_j}, \qquad {i,j=x,y,z}$$ (6.45)

the Born effective charge tensors

$$Z^*_{ij}=\frac{\Omega}{e}\frac{\partial P_i}{\partial u_j} =\frac{1}{e}\frac{\partial F_i}{\partial E_j}, \qquad {i,j=x,y,z}$$ (6.46)

and the ion-clamped piezoelectric tensor of the system

$$e^{(0)}_{ij}=-\frac{\partial \sigma_i}{\partial E_j}, \qquad {i=xx, yy, zz, xy, yz, zx}\quad{j=x,y,z}$$ (6.47)

from the response to finite electric fields. In this case, the "response" of the system is the change in the polarization $P$, the Hellmann-Feynman forces $F$, and the stress tensor ${\sigma}$.

To this end VASP will perform essentially three successive calculations, with:

EFIELD_PEAD= $E_x$ 0 0, EFIELD_PEAD= 0 $E_y$ 0, and EFIELD_PEAD= 0 0 $E_z$.

By default, VASP uses $E_x=E_y=E_z=0.01$ eV/Å. This default can be overwritten by specifying (see Sec. 6.67.3):

EFIELD_PEAD = $E_x$ $E_y$ $E_z$ (eV/Å)

The relevant output is found in the OUTCAR, immediately following the lines (see Sec. 6.72.4 as well):

MACROSCOPIC STATIC DIELECTRIC TENSOR (including local field effects)

BORN EFFECTIVE CHARGES (including local field effects)

PIEZOELECTRIC TENSOR (including local field effects)

In the above, "including local field effects" pertains to the fact that changes in the orbitals due to the electric field induce changes in the Hartree- and exchange-correlation potential. One may choose to limit this to changes in the Hartree potential alone, by specifying:

LRPA=.TRUE. (Default: .FALSE.)

This is commonly referred to as the response within the "Random Phase Approximation" (RPA), or the "neglect of local field effects". The OUTCAR file will now contain additional sections, headed by the lines:

MACROSCOPIC STATIC DIELECTRIC TENSOR (excluding local field effects)

BORN EFFECTIVE CHARGES (excluding local field effects)

PIEZOELECTRIC TENSOR (excluding local field effects)

N.B.: For standard DFT functionals $\epsilon_\infty$, $Z^*$, and $e^{(0)}$ may be more easily calculated from density functional perturbation theory (LEPSILON=.TRUE., see Sec. 6.72.4). For functionals that depend not only on the density but also explicitly on the orbitals, like hybrid functionals, density functional perturbation theory is presently not implemented and LEPSILON=.TRUE. is not applicable.